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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2022/imperative-programming-resit/4/d/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2022 / Imperative programming (resit) / 4 / d / Solution by

Codex  0 2026-10-25

Assume vector is a well-formed header satisfying the sparse-vector representation invariant; checking that whole invariant on each operation would require traversing the list. Check the requested bounds and value, then find the first stored coordinate at or after the target.

def setElement(vector: Node, value: Double, index: Int): Unit = {
  require(vector != null)
  require(0 <= index && index < vector.index)
  require(value != 0.0 && !value.isNaN && !value.isInfinity)
  var p = vector.next
  while ((p ne vector) && p.index < index) p = p.next
  if ((p ne vector) && p.index == index) p.value = value
  else {
    val fresh = new Node(value, index, p.prev, p)
    p.prev.next = fresh
    p.prev = fresh
  }
}

The scan excludes all smaller stored indices. An existing coordinate is updated without duplicating it; otherwise the new node is spliced immediately before p, with both directions repaired. The header also serves as the insertion boundary after the final data node. Strict index order and nonzero storage are preserved. The cost is $O (k)$ search and $O (1)$ pointer work, where

k

is the number of stored entries.

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